This equation will change how you see the world (the logistic map)
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День томуThe logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: www.fasthosts.co.uk/veritasium Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself: github.com/jonnyhyman/Chaos
References:
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976). doi.org/10.1038/261459a0
Robert Shaw, The Dripping Faucet as a Model Chaotic System
archive.org/details/ShawRober...
Crevier DW, Meister M. Synchronous period-doubling in flicker vision of salamander and man.
J Neurophysiol. 1998 Apr;79(4):1869-78.
Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns Cogn Neurodyn (2012) 6:89-106 DOI 10.1007/s11571-011-9184-7
A Garfinkel, ML Spano, WL Ditto, JN Weiss. Controlling cardiac chaos
Science 28 Aug 1992: Vol. 257, Issue 5074, pp. 1230-1235 DOI: 10.1126/science.1519060
R. M. May, D. M. G. Wishart, J. Bray and R. L. Smith Chaos and the Dynamics of Biological Populations
Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 27-44
Chialvo, D., Gilmour Jr, R. & Jalife, J. Low dimensional chaos in cardiac tissue. Nature 343, 653-657 (1990). doi.org/10.1038/343653a0
Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51-60
Libchaber, A. & Laroche, C. & Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. dx.doi.org/10.1051/jphyslet:01.... 43. 10.1051/jphyslet:01982004307021100.
Special thanks to Patreon Supporters:
Alfred Wallace, Arjun Chakroborty, Bryan Baker, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Lee Redden, Lyvann Ferrusca, Michael Krugman, Pindex, Ron Neal, Sam Lutfi, Tige Thorman, Vincent
Special thanks to:
Henry Reich for feedback on earlier versions of this video
Raquel Nuno for enduring many earlier iterations (including parts she filmed that were replaced)
Dianna Cowern for title suggestions and saying earlier versions weren't good
Heather Zinn Brooks for feedback on an earlier version.
Music from:
epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4"
ve42.co/Artlist "Busy World" "Children of Mystery"
@tanvisharma6903 3 роки тому
Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.
@realdanrusso 3 роки тому
yeah i made it 8 minutes in --with so much struggle-- and then blew up
@ashfujiyama 3 роки тому
this is such an underrated joke
@caturlifelive 3 роки тому
up
@gingaming_gg 3 роки тому
Pretty much 😂😂😂
@depressedguy9467 3 роки тому
Go back
@AustenAlexander 4 роки тому
Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on
@nickreed7277 4 роки тому
Damn dude. your elementary had algebra? i didnt get to that till highschool
@Matt_10203 4 роки тому
@@nickreed7277 or he means that it is elementary level algebra, not in relation to schooling, just that he struggles to understand the basics of algebra
@Edlundd 4 роки тому
Bro I dont even know what algebra means
@JoeyLovesTrains 4 роки тому
Lol I got algebra in 8th grade in Middle school But my class was the only one, everyone else had pre-Algebra
@luppa79 4 роки тому
Verisatrium :)
@user-qx5cn1si1q Рік тому
Things like these actually make our world more magical than any science fiction
@glowerworm Рік тому
We're living in a simulation and the 4.669 number just happened to be one of the global variable definitions.
@ihatemicrosoftsobadly3188 Рік тому
@@glowerworm Dear matrix guys don't use global variables it's bad practice
@glowerworm Рік тому
@@ihatemicrosoftsobadly3188 lmao, maybe it's destiny that every programmer, no matter how powerful, will write bad code.
@ihatemicrosoftsobadly3188 Рік тому
@@glowerworm so true ... ;)
@justpassingbyy Рік тому
@@glowerworm Shoulda been 4.2069 imo
@brucefoote540 Рік тому
Your 3 dimensional animation of the rotating Mandelbrot Set graph conveys so very much information and complexity. Amazing!
@ingridfong-daley5899 4 місяці тому
YES! Thank you for such well-constructed visualisations. They really are like compact little gold mines of information. :)
@3orM00Rrecharacters 4 місяці тому
I’m an artist and took screenshots of the set graph and logical equation as inspiration. Data really is beautiful.
@ingridfong-daley5899 4 місяці тому
OMG i took screenshots as well :) Agreed--data IS lovely.@@3orM00Rrecharacters
@HiManLOL 4 місяці тому
people out there proving existance of god with Mandelbrot fractal
@convolutionality 4 місяці тому
its so pretty my inspiration too
@ColorwaveCraftsCo 3 роки тому
The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen
@erteple2647 3 роки тому
looks like a deformed pringle
@benhsuan4817 3 роки тому
That and the "shadow" of a 4-dimensional cube passing through 3 dimensional space are the coolest mathematical animations I've seen. Matt parker shows it at the end of his talk at the Royal Institute if you're interested.
@mizomint4197 3 роки тому
But... Humans can't see in 3D... So... Have you really seen it?
@bestawdomx6835 3 роки тому
@@erteple2647 there is infinite?
@steveskeletonne-7394 3 роки тому
ukposts.info/have/v-deo/cYVhjIybrYeoon0.html This is essentially just a bunch of 3D fractals.
@entropy_7827 3 роки тому
Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.
@FunTheMentalist 3 роки тому
when he rotated the Mandelbrotset on the z axis, i felt that
@kumarsaieshrane9692 3 роки тому
😂😂😂😂
@masterpsk 3 роки тому
I did the "Keanu whoa" follow by a long "Duuuude!"
@gangsta6730 3 роки тому
I was like "hol up-"
@eusebiorozco 3 роки тому
Hahahahaha
@zanityedpo1398 9 місяців тому
When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained 💜
@strayspark1967 7 місяців тому
i've had a similar experience, now explained 30 years later......strange world we live in, everything makes sense, eventually
@dmajorvgm8735 4 місяці тому
The video didn’t really explain the behaviour though, it just made an observation/comparison to the mathematics they were talking about. I’d be interested in a more in depth video that actually explains why we see this behaviour so often
@nu1x Місяць тому
@@dmajorvgm8735 Well, noone knows WHY, people just noticed where it matches the algorithm. And why may be, I strongly suspect, some extremely fundamental basis on which the whole reality has existence, hence why this video is quite startling.
@joekelley5121 Рік тому
I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.
@mikeinjapan2004 4 місяці тому
Good point. But there are people who can actually connect those things naturally. I think this is also a skill on its own - we don't need to be thought because we see those patterns interacting each other and what have presented seems to be trivial...
@stiefjac5082 4 місяці тому
100% i always thought that we would have leaps and bounds of breakthroughs in understanding the entire structure of the universe if we taught students in school basic math... and then showed them crazy concepts like these in the hopes that one of the billions of people on the earth will see them and go "huh that reminds me of x, what if we apply it here?" rather than pushing them through advanced mathematics to get degrees not only that but if you look up slow motion explosions on youtube and look closely the inital explosion looks like the mandelbrot set, and you can see that as it expands there are little bits of contraction in every single explosion if you take it frame by frame i watched this video when it came out 3 years ago and i've been obsessed with the concept ever since
@ADUAquascaping 4 місяці тому
@@mikeinjapan2004You probably notice all of the 25+ functions within plasma/flame 😮😂
@va941 3 місяці тому
Guess you never did psychedelics while in school then😂😂😂
@piercelane7757 3 місяці тому
A lot of this video is centered in something you might find in a numerical analysis class. I just took one in college and we went over a lot of this kinda stuff.
@feynstein1004 4 роки тому
Numberphile: Makes video about the Feigenbaum constant Veritasium: Makes video about the Feigenbaum constant but includes the z-axis
@unathimatu 4 роки тому
it was a bifurcation
@BinyaminTsadikBenMalka 4 роки тому
@@unathimatu lol, perfect response dude!
@BasiC7786 4 роки тому
and then there's 3blue1brown telling you what PI has to do with all of this
@cezarcatalin1406 4 роки тому
Feigenbaum constant: Works for all recurrences that come from functions with a single hump. A mathematician: Well, we have to demonstrate that A computer scientist: Give me the Summit supercomputer for a few days to find a counterexample
@larrysal8866 4 роки тому
_mind blow_
@youmaybebusy 4 роки тому
"Oh cool, the Mandelbrot-Set. I have seen that before." *turns Mandelbrot-Set in 3D* "What the ...?! That's illegal!"
@DrIridium 4 роки тому
haha same
@scurvofpcp 4 роки тому
I know, right
@IRuinEvrything 4 роки тому
relatable
@smoothe14 4 роки тому
This is getting out of hand, now there’s two of them... wait four of them. Hold up. Eight of them... wtf a chaotic number set of them??!? This really is getting out of hand. Oh wait no just two of them.
@Uberkist 4 роки тому
mandelbulbs are gunna blow you away bro
@madeeb04 Рік тому
The fact that “chaos theory” is a real thing absolutely blows my mind. Even pure chaos can be mathematically modeled. Incredible.
@falcxne Рік тому
For anyone wanting to study the math of this, I recommend Steven Strogatz - Nonlinear Dynamics and Chaos. That was the textbook I used in undergrad.
@simrans3675 Рік тому
So, basically, 'Chaos' is a misnomer now. There is clear method and math to the madness. Are we really living in a simulation :-)? Sometimes, it fascinates me to see all the advancements made in math, science. probability. stats etc with a simple thesis to put some structure/framework to quantify the world around us. It has helped us explain a few phenomenons, create products, even predict stock prices, human behavior (looking at patterns and trends etc) but the other part of me is conflicted - for life and its energies cant be modeled. It's too fascinating to be modeled out and the vastness of the universe and my spiritual beliefs are a complete anti-thesis to my scientific side. Heck, even science is ever changing - now, we are discovering qubits - particles that carry both -ve and +ve charges, which has deep implication to our view of physics and the world around us! While amazing, how much can humans really 'figure out' vs realizing there is something more to life that what even our more prolific attempts at math/AI/ML will ever get us to.. Or, perhaps, there isnt a higher power :-)?
@roshnirana2098 4 роки тому
2019:- so this is aerogel 2020:- let's throw a little chaos at children and each other
@AngelOrtiz-wt7xt 4 роки тому
Roshni Rana aqq msm
@zperdek 4 роки тому
Chaos is magic.
@PavR376 4 роки тому
Hey we have the same last name, first time I've meet one online
@user-pj8mt2kd4v 3 роки тому
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@BAgodmode 2 роки тому
When you turned the Mandelbrot on it’s side to show the bifurcation, I’ll be honest, it blew my mind.
@jingalls9142 2 роки тому
That one made me stand up an pace frantically for awhile....mind blown..
@shadeop6773 2 роки тому
@@jingalls9142 same..... It blew my mind.
@asparagii 2 роки тому
yeah that was awesome
@carriersignal 2 роки тому
Same here. Had to stop it and sit back in my chair. Perhaps this is well known, but this is the first time I have ever heard of it.
@r0flcats 2 роки тому
Its now my wallpaper!!! That image its insane
@maegodragon Рік тому
Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!
@marco-salfi Рік тому
You a rabbit by any chance
@hugojj101 Рік тому
You're heart chaotically fibrillated, you maybe dying haha. Nah that's mad though. If you're heart did actually double beat, that was literally an example of the video. So strange, and even stranger that complex numbers that exist on a plane we can't see are linked to all our hearts and the rest. One day we'll understand maybe. hah
@BanditMatt Рік тому
Currently writing a report on chaotic behaviours and bifurcations, remembered this video existed and im so grateful now
@Chord_ 2 роки тому
"I'm so excited about chaos" -man one month into 2020
@maumau9466 2 роки тому
Lmao😂😂😂
@norpriest521 2 роки тому
@@maumau9466 What that means
@starryepidemic2532 2 роки тому
@@norpriest521 it means laughing my ..... Off and no im not gonna fill in the blanks
@koborkutya7338 2 роки тому
Well, it just tells us someone is messing with the parameters big time.
@MrSleepyweezul 2 роки тому
When things are chaotic, you focus on chaos. And when you focus long and hard enough, even chaos can make sense.
@garfieldturismo 4 роки тому
Everyone here were gangsta till he turned the Mandelbrot-set 3D
@cfneal1459 4 роки тому
Explain? Please.
@doctorquantum3364 4 роки тому
@@cfneal1459 r/woosh
@jinx5349 4 роки тому
@@doctorquantum3364 you can't woosh someone for wanting an explanation.. 🙄
@rohangaikwad255 4 роки тому
Hahaha
@maxlank539 4 роки тому
I'm dead 😂😂😂😂
@jeff_tj Рік тому
That book is amazing - and you have done it justice. That 3d graph was awesome!
@jawadfarrukh6736 Рік тому
Do you know which software did he use?
@Peace2051 10 місяців тому
Thank you for making some fundamental mysteries of math/nature at least approachable if not fully understandable to the general public. Great job!
@TheMsksk 4 роки тому
"How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!
@SergioEduP 4 роки тому
It lowered it for an 18 year old too =P maybe there are even younger people watching, and if there aren't we could share the video to them
@incription 4 роки тому
@@SergioEduP 17, beat that
@arvintis2293 4 роки тому
InCrIpTiOn 16.
@incription 4 роки тому
@@arvintis2293 I think krish beat both of us
@tomifiju 4 роки тому
@Krish Kalra yet here I am during meiozis I
@edstervedster 4 роки тому
6:40 When the animation showed the Mandelbrot set being related to the bifurcation diagram my mind was blown...
@elee9056 4 роки тому
edstervedster I WANT THAT MODEL AS A CHANDELIER. SO. BAD.
@carloshogar2 4 роки тому
Same here. I am fascinated by fractals and never knew this relationship
@airpolygon2714 4 роки тому
@@elee9056 you should make that idea a reality! I'd buy two
@rianby64 4 роки тому
The same happened to me! not sure if really they're related... must rewind and check it again.
@Cloud7050 4 роки тому
Crowdsourceeee
@Sagitarria Рік тому
You really did a good job with this one. This is something that’s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didn’t believe me! This stuff seems so fundamental, but it doesn’t seem like it’s tot as a unifying principle when it could be. It’s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.
@magic.marmot Рік тому
I've been studying emergent behavior since the 80's, when I first read Conway's Game of Life. Back then, it was treated as a nuisance, irrelevant, and annoying. I love watching the break into oscillation as your R-value changes .That's the same behavior as a damped spring, or feedback in an audio system. The transition to chaos between states makes a lot of sense. I love the visualization of the Mandelbrot set, that gave me the perfect starting point to understand it in another dimension. Wonderful.
@jemert96 2 роки тому
*_rotates the Mandelbrot plot_* Everyone: "wait what's he doing" Me: "he's beginning to believe"
@futurefacts6909 2 роки тому
hahahahaha
@futurefacts6909 2 роки тому
is it normal this video gave me goosebumps ?
@londonkoster3888 2 роки тому
@@futurefacts6909 yes
@jvm53 2 роки тому
yeah, you are special...
@londonkoster3888 2 роки тому
@@jvm53 she is
@DanielSmania 3 роки тому
I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!
@mackhomie6 3 роки тому
i want this guy on my team after a nuclear holocaust. me and a bunch of mathematicians.
@MoorganHart 3 роки тому
Yeah, another well done video. I am left wondering the relevance of the Mandelbrot Set though. I'm not a mathematician, and I've never heard of it before. I'll do a web search, but would have liked to hear about where the equation came from within the video.
@Polarwhisper6 3 роки тому
I think you meant: "I am 'A' mathematician"
@christianmathison5892 3 роки тому
@@Polarwhisper6 he didnt claim to be an english major
@Sergiuss555 3 роки тому
@@christianmathison5892 to be fair there could be girls among those mathematicians.
@rianschoeman559 Рік тому
James Gleick's book is really good. Once in a post office que I observed someone putting a fan on a scale. The reading bifurcated. I asked her to set the fan to a higher speed. The reading bifurcated again between four readings. I was blown away.
@Prophet_Isaiah 10 місяців тому
So cool
@penguinswithpencils2333 4 місяці тому
I ran across this video about a month into my discrete dynamical systems course. It has been super helpful to have something that gave me some intuition surrounding these patterns before I encountered them formally in class. Sharing it with my professor now :)
@ShiftK 3 роки тому
**slightly opens kitchen faucet* Me: I'm somewhat of a scientist myself
@bilalthefighter829 3 роки тому
lmao
@treewizard4508 3 роки тому
Have you written a scientific paper?
@Hwywbwjw 3 роки тому
Tree Wizard wat
@ginoyesano5649 3 роки тому
Your comment fits your profile picture so well 😂
@Hapasan808 3 роки тому
*slightly opens kitchen faucet * Me in a Joker voice: "I'm an agent of chaos."
@blobishlybelfer2717 3 роки тому
thanks for showing me that as a child i had absolutely no chance of predicting when a water drop will drop.
@K3zz21 3 роки тому
"when a water will drop" a SINGLE water
@who-ow5ix 3 роки тому
😂😂
@plaverbach 3 роки тому
@@K3zz21 When the water would drop?
@zacharyhall7466 3 роки тому
Chaos theory?
@haydenbellis3047 3 роки тому
.Turn to United Brethren Church. Using the Lords name in vain is a sin and so is cursing upon your enemies. And so is saying anything hateful, premarital sex and lust are all sins..⁰
@amanuka291 Рік тому
I can't even describe how amazed I am. Thank you for this video! It was a huge help with my studies and such an entertaintment!
@jaianupamvarun8722 Рік тому
I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately 😃❤️💕
@warrenchinn4114 3 роки тому
Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !
@warrenchinn4114 3 роки тому
@@shyamkarthikeya4769 That was my point ... :)
@supteg2.495 3 роки тому
@@warrenchinn4114 again a smart man..
@genericusername4206 3 роки тому
Warren Chinn true
@bfern053 3 роки тому
@@shyamkarthikeya4769 delete this
@DickEnchilada 3 роки тому
I learned about this constant (and the equation) when I was taking a System dynamics course 2 years ago. Absolutely loved that course. Stay learning dude!
@JohnSmith-gs4zv 4 роки тому
13:57 "What _really_ *IS* a faucet?" - Vsauce music starts
@impanthering 4 роки тому
ok John Smith
@calix451 4 роки тому
I miss him
@geekjokes8458 4 роки тому
But his video would actually *start* liake that And finish by talking about *UNIVERSALITY*
@DrSpooglemon 4 роки тому
"This is water dripping from a faucet. OR is it?!"
@ricardopieper11 4 роки тому
I read the first 3 words of your comment in michael's voice before acknowledging the word "vsauce" in it
@samuellafleur890 6 днів тому
Having just watched your video on the ubiquity of 37, I couldn't help but notice that was the first example you provided when taking about period doubling sequences of any length!
@nsfa19 21 день тому
This has got me really interested and fascinated as well. Congrats on such high quality top-notch videos! Thank you very much!
@DreamLoud05 4 роки тому
THat was definitely one of the shortest 18 minute video I have ever watched on youtube. Very fascinating
@FnaticKiller 4 роки тому
Now that is a compliment.
@IRL.johnny 4 роки тому
this is frighteningly true... I watch it at 1x while my wife brushed her teeth... how's that possible?
@diabl2master 4 роки тому
wtf, I did not realise that was 18 minutes, I was totally enthralled
@pdutube 4 роки тому
If you observe a subject watching this video at a specific fraction of the speed of light, you could see it at 18 minutes no matter what the subject's playback speed was.
@liqwiz 4 роки тому
I felt Exactly the same. Only by reading your comment I realised "wait... That was almost 20 minutes?"
@sloanehowell6166 3 роки тому
“When this baby rotates on the z-axis, you’re gonna see some serious sh*t.” - Dr. Emmett Brown
@davememelandcanada6722 3 роки тому
We don't talk about the Doc, since he f**ked up the timeline for 2020.
@chop-daresistance7514 3 роки тому
Wow doc.. that's heavy
@chop-daresistance7514 3 роки тому
@@davememelandcanada6722 I don't think that was doc.. I think that was biff when he stole the DeLorean
@anasaamir5595 3 роки тому
wht is z asix
@Leosayshi 3 роки тому
@@anasaamir5595 If I had to guess it’s probably another axis like the y and x axis except it’s used for 3D shapes.
@shamsamir1698 Рік тому
One of the most beautiful videos on youtube! keep getting back to it every time.
@nfc14g Рік тому
Feels like when you are using exponential equations your inputs are very important and deserve a lot of explaining why you chose it, regardless of real value or best estimate value
@briancherry8088 4 роки тому
8:43 - Boom. Mind blown. We've been missing the 3rd dimension of the Mandelbrot set this whole time.
@mikeciul8599 4 роки тому
Actually, I think there might be a 4th dimension, because for some complex values of c, the equation could converge to complex numbers.
@DemonSwrd 4 роки тому
now imagine the 4th dimension.
@briancherry8088 4 роки тому
@@DemonSwrd - no. The world will explode.
@hammerth1421 4 роки тому
@@mikeciul8599 It is the real part of the complex value returned from the complex logistic map. If the result was also complex the Mandelbrot set would be 4D.
@brando3342 4 роки тому
@@DemonSwrd We can't imagine that. That's like asking someone to imagine a one dimensional point. Yes, some cosmologists want to say that was what the singularity was at the beginning of the universe, but think about it, it doesn't make sense.
@andriypredmyrskyy7791 4 роки тому
As a control systems engineer, I've seen this behaviour before in several systems when control goes awry. Now that I know there might be something I can do about it, this opens up all sorts of possibilities to new control methods. I'm freaking out a little bit.
@Rotem_S 4 роки тому
Actually the first physical chaos measured was an engineer using a simple circuit with a transistor and a harmonic input, where he sometimes saw one period, sometimes two, and sometimes all of them
@austinwessels 4 роки тому
I was thinking about controls too for most of the video!
@revenevan11 4 роки тому
Wow, you could control something back from the edge of chaos or even from already started chaotic behavior (like an airplane already entering an aerodynamic stall) using the methods that those scientists used on the rabbit hearts! I hope you're looking into that paper right now lol.
@brocktechnology 4 роки тому
I'm no engineer, but I'm right there with you. I was hit by the realization that this little bit of math is the reason PID is so difficult to do well.
@revenevan11 4 роки тому
@@brocktechnology I'm super excited for the possibilities of better control algorithms by using something analogous to the research in restabilizing heartbeats, the implications are awesome for aerospace engineering.
@harshildobariya6773 10 місяців тому
One of the most mind-bending concept I have came across. I love your channel, it is one of the best.
@Khpr666 Рік тому
Bro! I love you! Thank you! Your work is increasing the growth rate of knowledge.
@sidsixpoint7 3 роки тому
Jokes on you, this didn't change the way I see the world because I'm dumb.
@HerGatiox 3 роки тому
at least you see that. You know that you don't know anything. congrats
@gabeharrison7683 3 роки тому
@@HerGatiox a bit condescending
@Zain69z 3 роки тому
Lmao
@aaroncruz9181 3 роки тому
You see math without numbers
@BenDover-vh9rs 3 роки тому
@Majin Buu then how tf does he know that?
@MrTigershark11 4 роки тому
6:37 One of the best plot twist I've seen in my entire life
@snowfloofcathug 4 роки тому
Hereizer Oh that pun is wonderful
@madalinspoiala1249 4 роки тому
You need to be higher. Great pun
@theshocktart 4 роки тому
Such a legendary comment, bravo...bravo!
@justarandomdood 4 роки тому
Dad joke levels are through the roof
@NiranjanDixit23 4 роки тому
Get out lmao
@potat8089 Рік тому
I remember watching this video when I was about 14 years old and being fascinated by this, but my understanding kinda dropped off when the Mandelbrot Set came into the video (I knew nothing about it). Rewatching this video at age 16, I can really appreciate it so much more, now that I understand it. Thank you for introducing me to the Logistic Map!
@matgeezer2094 Рік тому
Again, did not expect to be blown away but am utterly. Superb video, bringing quite a 'dry' subject alive.
@belgianbushrc7934 3 роки тому
I am intelligent enough to find this interesting but not quite smart enough to fully understand... Great video!
@eletinalex 3 роки тому
covid-19= this is control over the rabbit population
@naturelovingfroggy6348 3 роки тому
Well said, me too x
@shadowpresident4203 3 роки тому
That's probably the ideal situation. If a tutor were to customize a lesson for you specifically, they'd probably aim for a difficulty level you'd find interesting, and a lecture that you could mostly follow. You'd also be very slightly outside your comfort zone, to give you room to "grow into" the lesson. It would also be a bit challenging and would leave you with a few questions to mull over, thereby slightly increasing the chance of watching another video, or of reading a book or article on a similar topic. Your comment would probably be music to the ears of a lot of educators.
@eletinalex 3 роки тому
@@shadowpresident4203 thx
@comet1954 3 роки тому
I feel your pain! I truly do....
@TehmasKhan 4 роки тому
You know the video is good when it’s 18:39 minutes long and you still didn’t want it to end
@za012345678998765432 4 роки тому
I didn't even notice until you pointed it out, thought it was like 9 minutes
@MartinBuzon 4 роки тому
@@za012345678998765432 I was going to say 9 too. Damn witchcraft.
@za012345678998765432 4 роки тому
@@MartinBuzon Next thing you know Derek comes here and tells us that this equation can explain that as well and it was all planned from the start XDD
@setsugennoao3137 4 роки тому
@@za012345678998765432 same
@KillaahMusik 4 роки тому
It felt like 4,669 minutes
@namakoro_osu Рік тому
since the start of the pandemic i have come back to this video time and time again and it was the first video i watched of yours and every time i rewatched it i under stand just a little more thank you for making many complicated topics over the years bite size and understandable
@IIronyy Рік тому
Dude I have absolutely no idea of anything I just heard but I still listened all the way through it takes a very talented type of person to intrigue his audience that much.
@bradleyewoodworth 3 роки тому
Out of all of the UKposts channels that I don't understand, this one is my favorite.
@zaphodsbluecar9518 3 роки тому
ROTFL - Nice work Brad! :-)
@AzTech71 3 роки тому
Lol
@Streamwalker1000 3 роки тому
LOL ! I'm with you on that.
@simphiwenxumalo4387 3 роки тому
@@Streamwalker1000 LOL me too
@johnmartin9451 3 роки тому
I'm sure you understand more than you thought, otherwise you wouldn't be drawn in. It's about patterns and randomness and how the two shall not meet.
@g0g0duck20 4 роки тому
Me: Watches video because I think I'm smart My brain: Hold on there buckaroo
@paratame105 4 роки тому
I feel attacked
@AverageAlien 4 роки тому
Don't worry we're all retarded here. Welcome to the club.
@Dontlagmebro 4 роки тому
Well how do you think (we) get smart?
@trevsanna 4 роки тому
LOL....You can actually apply the equation to your comment to see how funny your comment actually is! :)
@rznleagueoflol4545 4 роки тому
Trevor Baylis no u cant
@vishalrander9805 Рік тому
Very much obliged to watch your videos. Thank you for making the complex to simple .
@jfidel3943 Рік тому
I love James Gleick's Chaos book. It's such an amazing book and I always learn something new from it.
@CHLOCHLOLP 3 роки тому
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
@CHLOCHLOLP 3 роки тому
@chcpr1 i think its more that no one in power cares to invest in school systems to make them better, but I dont think they are shitty on purpose, just due to neglect. Why would rich government officials care about public schools when are their kids are privately educated anyways, you know?
@Eden894HisBiome 3 роки тому
Yeah sadly they don’t teach you anything your not tested for. Unless they a good teacher.
@kaffeetasse9455 3 роки тому
One of my teachers actually showed us the mandelbrot set and told us about chaos teory. :D
@chrisbarber7291 3 роки тому
Um, they do teach this.
@sirxobsidian408 3 роки тому
Unfortunately, this simply isn't true. I'm a high school math teacher, and I've shown this kind of thing to my students on numerous occasions, and the response is pretty much always the same; disinterest. If it's not on a test, they see it as an excuse to take a nap, zone out, or work on other classes' assignments.
@RPS2443 4 роки тому
"The mandelbrot set is numbers that don't blow up" Mind blows up. Seriously the best explanation ever. Then he shows it in 3d. Learned more in 20 minutes than in the last 20 years.
@userMikeforsure1997 4 роки тому
I felt that.
@hannesthurnherr7478 4 роки тому
so your saying your mind doesnt belong to the mandelbrot set?
@kennyogbogu7777 4 роки тому
Now that's funny.
@RPS2443 4 роки тому
@@hannesthurnherr7478 Well, rules are rules, so apparently you are right!
@mihalykort84 Рік тому
I went to the "Chaos Conference" at Sydney in (I think?) 87, met some pretty incredible physicists and mathematicians, and even got a couple of Autographs :) but mostly felt just awed that this was an interesting thing, and that I knew somehow it also was kind of important. B Mandelbrots lecture was lovely, but some of the different maths topics (from geometry obviously, but Prime number theory, Analytic and Discrete maths and biological mathematics. For me it was a memorable experience. So I get you, and I wish you more power to your arm, because yeah there's something compellingly beautiful and yet still mysterious. Good on you for your work, long may you continue and thanks!
@KM-co5mx Рік тому
We need more videos like this! ⭐️
@Hgulix62 4 роки тому
This is like when you start a new project or new year resolution. Everything is fine and simple at first, then progressively and unexpectedly everything turn to chaos
@eternalexperience2489 4 роки тому
Probably the rate of degradation is 4.669 :o
@somethingtojenga 4 роки тому
"How did I get to be 37 years old without hearing about the Feigenbaum constant?" That is an extremely optimistic outlook on what 37-year-olds should be concerned about.
@djb903 4 роки тому
I turned 37 yesterday and I'm glad I've heard of it thanks to Derek
@arvind8302 4 роки тому
SomethingToJenga 100%
@binashah3106 4 роки тому
well im 7
@spb1179 4 роки тому
Bina Shah good keep learning. You might be remembered for something awesome if stuff like this interests you!
@binashah3106 4 роки тому
jk im 13
@iamlubos Рік тому
Great video! It's also a really good subject for a take-home final exam in a scientific computing class I am teaching this semester.
@VisualJoey Рік тому
You definitely did this topic justice in my personal experience! Thank you (…) And this is just one topic where you do justice. I don’t practice maths nor more of the topics you have covered. At least, in a professional or study kind of way that is. However, I have found your explanations to be inspiring and fascinating. You really hit a spot of interest of which I have always had an interest for but never got my head to understand due to the complexity. It’s a gift to be able to watch your videos and get a grasp of understanding. Even though sometimes the grasp barely touches the surface.
@t-riz7630 4 роки тому
Me: cannot do basic calculus *sees title of video* UKposts just gets me.
@BudEnzo 4 роки тому
I taught myself basic calculus from videos on UKposts. Both Khan Acad and 3blue1brown really helped. I was able to skip Math 251 (Calc 1) at my college and move straight to Calc 2 after a 4-year break between studying BASIC algebra in high school and returning to college.
@tishafeed8085 4 роки тому
@@BudEnzo wait what, you studied basic algebra in high school?
@BudEnzo 4 роки тому
@@tishafeed8085 I guess lol. My school called it pre-calculus so basically it was algebra+trig.
@tishafeed8085 4 роки тому
@@BudEnzo what years/classes? in my highschool (9th-11th year) we did trig+calculus
@tishafeed8085 4 роки тому
@gamecube.enthusiast - - i did, but the fundamentals were studied in years 5-9, then it was trigonometry and calculus. Actually, i just realised it depends on what you call 'highschool'
@CuteC3 3 роки тому
So basically like when the bass drops, the tempo keeps doubling until it just goes into complete madness.
@Cher007 3 роки тому
The 101 of Speedcore and Splittercore 😂
@sethreardon8805 3 роки тому
Something tells me that you might have said the smartest thing in these comments. Music is vibration, vibration is periodic. This equation probably can be found in music somewhere...
@TheMaxwellee 3 роки тому
I hope a nerdy DJ builds his set this way
@StormEngineer 3 роки тому
I almost spit my coffee. Well done.
@RCFrizz 3 роки тому
@@StormEngineer Imma go brew some coffee so I can almost spit it!
@lintonatlas8933 11 місяців тому
Outstanding explanation of chaos theory. I especially liked the unifying of the madelbrot set diagram and the doubling diagram, I don't recall seeing that before.
@preranaprasaddeshmukhbe20b34 5 місяців тому
This is one of the most amazing video I had seen on UKposts till now
@infinitiv525 4 роки тому
I am so glad that some lad just woke up one day and decided: "You know what, I should do some research of dripping faucet."
@TheFredmac 4 роки тому
That would be a lad that doesn't get government funding.
@blackdaan 4 роки тому
weed is good for some things...
@rtleitao78 4 роки тому
You mean, instead of fixing it?
@BenjaminCronce 4 роки тому
you mean "woken up by a dripping faucet"?
@slaughterround643 4 роки тому
Veritasium: "Students can have a little chaos, as a treat."
@joshgiesbrecht7060 4 роки тому
literally my teaching strategy
@AaronRWilliams97 4 роки тому
*little a chaos
@bengardner8639 4 роки тому
If you're gonna reference the meme, at least do it right. It's "little a", not "a little".
@marcushendriksen8415 4 роки тому
Make them climb a ladder for it, though
@AaronRWilliams97 4 роки тому
Ben Gardner *le sigh* He DID say pedants were necessary..
@Elletanvilla Рік тому
Thank you so much for this video!!! I can’t understand it fully but my God it still moved me to tears
@DavidMauas Рік тому
This is really mind-blowing, I absolutely love it!
@vincenzkoop43 3 роки тому
6:43 most underrated placement of the term ‚plot twist‘
@wedantil 3 роки тому
Pun of the day!!!!
@kennethsizer6217 3 роки тому
I love you, man!
@Surya-jz6te 3 роки тому
german?
@cadosian078 3 роки тому
Top 10 anime betrayals
@snowstarsparkle 3 роки тому
i don't get it, please explain !
@PietchRhum 4 роки тому
I feel so dumb! I have a PhD in Ecological Modelling, I have used this equation - and more complex version of it - to model population dynamic multiple time and I didn't knew of this Feigenbaum constant!!! I had teaching on Chaos and none of my professor mentioned it! Well, thanks Veritasium for teaching us new things!
@KarasuInaiga 4 роки тому
P. V. I read that as “Executive Meddling”.
@metanumia 4 роки тому
@@KarasuInaiga 🤣
@spencerquirk6917 4 роки тому
@@KarasuInaiga 🤣🤣🤣
@BrandonRx2 4 роки тому
Huh
@ansh6370 4 роки тому
Bruh I'm just an eight grader. Tomorrow's my maths test and I'm supposed to learn mensuration and algebra but I'm here trying to figure out what this video even is about after watching it for the 7th time.
@mikedavies5551 4 місяці тому
Brilliant especially the final part about different functions. That is new to me. Thanks.
@pudayshankar1036 Рік тому
Your videos never failed to make me think about what is the purpose of this universe.. why is it there and how it works so perfectly without anyone controlling it..
@locotx215 4 роки тому
6:41 - "The Plot Twist" figuratively and literally
@aliffikri1888 4 роки тому
Noice
@himagnamukherjee9382 4 роки тому
pure gold
@carsonmorris127 4 роки тому
This whole video is a plot twist
@papa_pt 4 роки тому
bravo
@DoktorIgnaz 4 роки тому
HOLY
@farhan132_ 4 роки тому
The more I learn, the more I realize I don't really know anything!
@mdestwo 4 роки тому
Ah, so you really have been paying attention! That seems to be one of the more important lessons to learn in life. So, here’s to you, me, and everyone else realizing we know less and less each year! 😀
@farhan132_ 4 роки тому
@@mdestwo Well said!
@glaucovillasboas8212 4 роки тому
That's for sure. I always think I'm smart, but a year later I always remember how stupid and dumb I was, and it keeps repeating
@avikdas4055 4 роки тому
Exactly man. But now I'm 100% convinced that I know absolutely nothing.
@Kraflyn 4 роки тому
welcome to the club! :D
@rainthevaporeon7852 Рік тому
I've not shown any interest in mathematics (or physics for that matter) for a long while, and this somehow sparked up my interest in it again, thanks. Really fascinating stuffs
@rajeswaranparameswaran6611 11 місяців тому
Amazing quality of presentation! Besides being a scientist with msrcellius 'teaching' skills, you are a classic cameraman too! Grateful.
@veritasium 4 роки тому
Feedback from UCLA A/Prof Heather Zinn Brooks: "At first, it seems totally crazy that increasing r would lead to cycles... if it's describing population growth, why would a bigger r cause a drop in some years? In fact, the magic is in the (1-x_n) factor of the equation, which models a carrying capacity. The idea is that populations are typically resource-limited, so growth can only be supported up to a certain point. Once you think about that, it makes sense that huge growth rates could result in "boom and bust" cycles in the population, because the population would grow faster than their resources would support."
@shetty98 4 роки тому
1:30 @m in 🇮🇳
@NatePrawdzik 4 роки тому
I imagine increasing rabbits also increases wolves, so that probably factors in as well.
@timezone5259 4 роки тому
Yes
@gordonrichardson2972 4 роки тому
This topic came up when I was studying applied mathematics around 1980: en.wikipedia.org/wiki/Lotka-Volterra_equations
@11quinnjet75 4 роки тому
Can this be applied to the expanding universe? because it has a growth rate and if I remember right scientists think that that rate has changed?
@avrenna 4 роки тому
When the Mandelbrot set rotates: whooaaaahhhhh
@xiaoxiaoxiao686 4 роки тому
5erif meme echoes in my head...
@Adam_Bosscoe 4 роки тому
Right!?!?!!
@valentinbernard8126 4 роки тому
Yeh that was spectacular
@trickytreyperfected1482 4 роки тому
"You're not supposed to do that!"
@aurelia8028 4 роки тому
I swear to god, my mind was blown away by that! I had only ever seen the Mandelbrot Set as that 2 dimensional boundary thing, so seeing that it was actually a 3D-thing was insane
@darrenirwin5411 Рік тому
Fascinating! Thank you for this wonderful video.
@pablog80 4 місяці тому
I was already aware of some of this stuff bit had never seen it related so strongly as it is explained here. Amazing
@variable7833 2 роки тому
This feels like a window into a small part of how the universe works. Its kind of scary and exciting.
@robologo 2 роки тому
Yeah it's very strange... all these formulas that pop up everywhere. I think there's an explanation though.
@pablooo8280 2 роки тому
@@robologo have u tried psychedelic drugs? you actually start seeing these everywhere
@mysonandme8424 2 роки тому
@@pablooo8280 nobody has because drugs aren't real.
@obiwanjaco 2 роки тому
@@pablooo8280 no
@obiwanjaco 2 роки тому
@@mysonandme8424 yes
@lc7ineo 4 роки тому
I found this incredibly fascinating... but understood incredibly little.
@jakewatson1160 4 роки тому
I was interested in it but i will always hate math cuz ths made me fall asleep lol
@panpsalt6757 4 роки тому
I understood more than I want, but still less
@thechappist 4 роки тому
Yup! Make me want to go learn some math!
@thechappist 4 роки тому
I had to write some things down to look up definitions! But interesting
@unbiasedhuman1659 4 роки тому
Fibonacci equation.
@S.Ali_Almosawi Рік тому
After this video I was able to see John cena
@weo9473 6 днів тому
💀
@zx8979 Рік тому
Excellent video! A good video to let me know more about chaos after hearing it in class, while my teacher didn't say too much about it.
@phillipejane8423 4 роки тому
UKposts algorithm - 1st stage - sends to people who are actually interested in math. Less views 2nd stage - sends to related viewers. Less views but still constant. 3 stage - Sends to random people on their feed. Fluctuations in view cycle (no negative views so it shoots up) 4 stage (chaos) - recommends to people like me of all people. Millions of views
@tomas_horn 4 роки тому
top comment!!
@norahclarissa6352 4 роки тому
This observation is actually clever, considering that the algo is an AI
@manictiger 4 роки тому
Recursive view count increases!
@RahulKumar-sy4xg 4 роки тому
UKposts's algorithm decode!
@jordanponton255 4 роки тому
Stage 5: people in the Mandelbrot set
@Max_Jacoby 4 роки тому
- What is the answer to the Ultimate Question of Life, the Universe, and Everything? - 4.669
@jcornman24 4 роки тому
Nice
@mmmmmark9751 4 роки тому
It's 42......of course we really don't know what the question is.....(ps. it is 6x9.....which is why it's all fuk dup)....thanks Douglas
@contessa420 4 роки тому
Nice reference
@BinyaminTsadikBenMalka 4 роки тому
It's 3 Pi /2
@RagavPuli 4 роки тому
@@BinyaminTsadikBenMalka 1.5xπ
@rudyardkipling4569 Рік тому
Excellent video. The ubiquitous emergence of the Feigenbaum constant is just disturbingly, weirdly beautiful.
@keyvanmalaie Рік тому
That was really a fantastic! Thank you!! I got scared seeing the bifurcation for the first time!
@Jessicalc941 3 роки тому
Me: understands less than 5% of what he said Also me: life changed
@waterproof4403 3 роки тому
haha same
@physcedelicanvs 3 роки тому
u nailed it better.i only undestand 0.00001 percent and felt like im the descendant of euklides
@jerrythemagichamster8586 3 роки тому
The good part is that 5% of the universe is seeable matter sooo.. you understand now about .0025% of the universe.
@TheBrickagon 3 роки тому
I swear, seeing memes and reading comments make me feel that we all live the same life :))))
@waterproof4403 3 роки тому
@@TheBrickagon haha some what comforting
@liondeluxe3834 3 роки тому
This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.
@aion2177 2 роки тому
github link please?
@jamesfield5415 2 роки тому
I got obsessed too it’s mesmerising
@NovaWarrior77 2 роки тому
please let us know. I for one for sure want to see it.
@goutamboppana961 2 роки тому
the beauty come when u keep zooming it
@CrackedCandy 2 роки тому
Oh my, my heart is beating faster now, so, where can I see this art?
@NuhDhulMitrain Рік тому
I attend a lecture about chaos, first it was dull and now it has become very interesting and fun, also numerically solving equations and getting those pictures
@valiantwarrior4517 Рік тому
If you look at larger fractal patterns of the Mandelbrot set, you can get a cool “magic eye” 3D effect. Particularly one called “Seahorse Valley.”
@ShilpanGPatel 4 роки тому
I saw the video title and thought “oh suuuuure this will change my life”, but wow I did not expect to be so taken aback by this. Something so fundamental which I’ve never heard about before!
@ayaipeeoiiu8151 4 роки тому
Shilpan Patel so you should subscribe to numberphile
@hidjedewitje 2 роки тому
This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!
@DataJYdocs 2 роки тому
ie: the Lorenz Attractor.
@albertofoti4152 2 роки тому
Yep, I'm here because I'm studying for an exam ahah Non-linear Control and Aerospace applications
@GdeJ 2 роки тому
Here's another: Chua's circuit
@albertofoti4152 2 роки тому
@@GdeJ I am from Politecnico of Turin in Italy and we had the pleasure of having a lecture directly from Professor Chua. I think the Lorenz Attractor and the Chua Circuit are the most thought in control engineering degrees. Maybe talking about non linear systems behaviors we also have systems having limit cycles in the phase portrait, for example the Van Der Pol Oscillator
@GdeJ 2 роки тому
@@albertofoti4152 I'm from Federico II University! I just had an exam on non linear dynamics and control. Other than Van Der Pol oscillator, our professor mentioned also other relaxation-excitation oscillators, such as Fitzhugh-Nagumo and Hindmarsh-Rose models of a neuron.
@moumous87 Рік тому
After 3 years, watching it again. Love this video!
@yli5531 Рік тому
This equation has been used to study the spread of information on social media. But a differential equation was used instead of this difference equation. See Campbell, Arthur, Dina Mayzlin and Jiwoong Shin (2017), “Buzz Management", The RAND Journal of Economics.
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